Find an equation on the line. Write the equation using function notation

Question

Points (3,1) perpendicular to f(x)=-2+2

Answer 1

I'm assuming you meant (3,1) and perpendicular to f(x) = -2x + 2.

If f(x) has a slope, m, then the perpendicular to f(x) has the slope (-1/m).

So we need a line with slope (-1/-2) = 1/2. It has to go through (3,1), so we're going to use point-slope form:

(y - y₀) = m (x - x₀)

So the equation then becomes: y - 1 = 1/2(x - 3)

Answer 2

If your function f(x) is indeed f(x) = -2+2, then f(x) = 0, which would be a horizontal line superimposed on the x-axis. In that case any vertical like would be perpendicular to it. A vertical line would have the same x-value and thus would be a constant value as a function of y. The solution then would be f(y) = 3, a vertical line located at x = 3.

https://www.desmos.com/calculator/cbjy2vviqn

However, and I suspect this to be the more likely case, if your function f(x) is actually f(x) = -2x +2, then any line with the the inverse for m (slope) of your original function would be perpendicular. Since m = -2, any function with a slope of m = 1/2 would be perpendicular to it.

Now you can use the Point-Slope Form to get the equation for a perpendicular line going through P(3;1).

y - y1 = m ( x - x1 )

y - 1 = 1/2 (x - 3)

y - 1 = x/2 - 3/2

y = x/2 - 1/2

https://www.desmos.com/calculator/xepmawsl5v